1. Field of the Invention
The present invention is directed to combinatorial auctions and exchanges and, more specifically, to determining winning allocations in combinatorial auctions and exchanges.
2. Description of Related Art
Commerce is moving online to an increasing extent, and there has been a significant shift to dynamic pricing via auctions (one seller, multiple buyers), reverse auctions (one buyer, multiple sellers), and exchanges (multiple buyers, multiple sellers). These market types have also become key coordination methods in multi-agent systems. These trends have led to an increasing need for fast market clearing algorithms. Recent electronic commerce server prototypes have demonstrated a wide variety of new market designs, leading to the need for new clearing algorithms.
There has been a recent surge of interest in clearing combinatorial auctions where bids can be submitted on bundles of distinguishable items, potentially multiple units of each. There has also been recent work on clearing combinatorial reverse auctions and combinatorial exchanges. The clearing problem in a combinatorial market is NP-complete, inapproximable, and in certain variants even finding a feasible solution is NP-complete. On the other hand, markets where there is only one unit of one item for sale are trivial to clear.
Another type of market setting is the ubiquitous one where there are multiple indistinguishable units of an item for sale. This setting is common in markets for stocks, bonds, electricity, bandwidth, oil, pork bellies, memory chips, CPU time, etc.
The naïve approach to bidding a multi-unit market would require the bidders to express their offers as a list of points, for example ($2 for 1 unit) XOR ($5 for 2 units) XOR ($6 for 3 units), etc. The mapping from quantities to prices can be represented more compactly by allowing each bidder to express his offer as a price-quantity curve (supply curve for a seller, demand curve for a buyer). Such curves are natural ways of expressing preferences, are ubiquitous in economics, and are becoming common in electronic commerce as well.
In classic economic theory of supply and demand curves (called partial equilibrium theory), the market is cleared as follows. The supply curves of the sellers and the demand curves of the buyers are separately aggregated. The market is cleared at a per-unit price for which supply equals demand (there may be multiple solutions). This way of clearing the market maximizes social welfare.
However, it turns out that the auctioneer (that is, the party who runs the market—who is neither a buyer or a seller) will achieve greater (or equal) profit from the same supply/demand curves by reducing the number of units traded, and charging one per-unit price to the buyers while paying a lower per-unit price to the sellers. We call such pricing non-discriminatory because each buyer pays the same amount per unit, and each seller gets paid the same amount per unit. The auctioneer's profit can be further improved by moving to discriminatory pricing where each seller and each buyer can be cleared at a different per-unit price.
It is, therefore, desirable to provide a method for clearing, or determining the winning allocation, in a forward auction, reverse auction, or exchange, when discriminatory and non-discriminatory pricing are in effect, that maximizes a clearing surplus. Still other desirable features will become apparent to those of ordinary skill in the art upon reading and understanding the following detailed description.